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Find, in surd form, the value of cos165....

Find, in surd form, the value of cos165.

A.

14(6+2)

B.

14(62)

C.

14(62)

D.

14(6+2)

Correct answer is D

cos165=cos(180165)=cos15

cos15=cos(4530)

cos(xy)=cosxcosy+sinxsiny

cos(4530)=cos45cos30+sin45sin30

= (22)(32)+(22)(12)

= 14(6+2)